Journal articles: 'Symmetry'

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Ubaidillah, Firdaus. "FUNGSI SIMETRI TERHADAP GARIS x = a DAN SIFAT-SIFATNYA." Majalah Ilmiah Matematika dan Statistika 20, no. 2 (September 29, 2020): 45. http://dx.doi.org/10.19184/mims.v20i2.19623.

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An even function is a function with a graph that is symmetric with respect to the y-axis or the line x = 0. In this paper, we will introduce a more general function of the even function, we call it as symmetry function with respect to the line x = a, which is a function whose graph is symmetric with respect to the line x = a. This paper discusses the properties of the symmetry function with respect to the line x = a, which is derived from the pre-existing properties of the even function. Some of the results obtained above, the linear combination of the symmetry functions with respect to the line x = a is a symmetry function with respect to the line x = a and the composition of any function with a symmety function with respect to the line x = a is a symmetry function with respect to the line x = a. Keywords: Even function, a symmetry function with respect to the line x=a, symmetric graph

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Li, Chunbiao, Zhinan Li, Yicheng Jiang, Tengfei Lei, and Xiong Wang. "Symmetric Strange Attractors: A Review of Symmetry and Conditional Symmetry." Symmetry 15, no. 8 (August 10, 2023): 1564. http://dx.doi.org/10.3390/sym15081564.

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A comprehensive review of symmetry and conditional symmetry is made from the core conception of symmetry and conditional symmetry. For a dynamical system, the structure of symmetry means its robustness against the polarity change of some of the system variables. Symmetric systems typically show symmetrical dynamics, and even when the symmetry is broken, symmetric pairs of coexisting attractors are born, annotating the symmetry in another way. The polarity balance can be recovered through combinations of the polarity reversal of system variables, and furthermore, it can also be restored by the offset boosting of some of the system variables if the variables lead to the polarity reversal of their functions. In this case, conditional symmetry is constructed, giving a chance for a dynamical system outputting coexisting attractors. Symmetric strange attractors typically represent the flexible polarity reversal of some of the system variables, which brings more alternatives of chaotic signals and more convenience for chaos application. Symmetric and conditionally symmetric coexisting attractors can also be found in memristive systems and circuits. Therefore, symmetric chaotic systems and systems with conditional symmetry provide sufficient system options for chaos-based applications.

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KANEHISA, Hirotada. "Symmetric Instability without Symmetry." Journal of the Meteorological Society of Japan 83, no. 1 (2005): 129–34. http://dx.doi.org/10.2151/jmsj.83.129.

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Mirenkov, Valery. "DEFORMATION AS A PREPARING PROCESS FOR DESTRUCTION." Interexpo GEO-Siberia 2, no. 4 (2019): 170–75. http://dx.doi.org/10.33764/2618-981x-2019-2-4-170-175.

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Actual mining is accompanied with stress increasing and as a result increasing of developed space causes to deformation of rock with specialties, which brake the symmetry, obtained after statistic calculation. For horizontal working classic approach leads to calculation of symmetric relatively coordinate axes deformation. In that case boundary conditions and mechanical quantities, related to soling containing development, are sized in an arbitrary way. However, it is well known from in-situ observations that braking the symmetry and as a result caving starting happen in the most stressed point. According to used physical and mechanical laws, destruction occurs quite unpredictable and does not have single before determined behavior. As it supposed in the context of symmetric calculation, trying certainly carry out the destruction. Kinematic calculation of displacements, considering weight of rocks, has allowed to brake classic symmetry at calculation of roof and floor displacements and to get closer to understanding of mechanism of the deformation process. In the work isotropic solid with horizontal sunken working, which provides the most deformation symmetry at classic calculation, is considered. Introduction into consideration of dynamic of process of actual mining totally destroys built symmery of possible deformation providing destruction starting in the most stressed point. Dynamic is considered after single advance of support, sum of which additionally provides absence of the symmetry in the destruction process.

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Wang, Yifeng. "Symmetry and symmetric transformations in mathematical imaging." Theoretical and Natural Science 31, no. 1 (April 2, 2024): 320–23. http://dx.doi.org/10.54254/2753-8818/31/20241037.

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The article delves into the intricate relationship between symmetry and mathematical imaging, spanning various mathematical disciplines. Symmetry, a concept deeply ingrained in mathematics, manifests in art, nature, and physics, providing a powerful tool for understanding complex structures. The paper explores three types of symmetriesreflection, rotational, and translationalexemplified through concrete mathematical expressions. Evariste Galoiss Group Theory emerges as a pivotal tool, providing a formal framework to understand and classify symmetric operations, particularly in the roots of polynomial equations. Galois theory, a cornerstone of modern algebra, connects symmetries, permutations, and solvability of equations. Group theory finds practical applications in cryptography, physics, and coding theory. Sophus Lie extends group theory to continuous spaces with Lie Group Theory, offering a powerful framework for studying continuous symmetries. Lie groups find applications in robotics and control theory, streamlining the representation of transformations. Benoit Mandelbrots fractal geometry, introduced in the late 20th century, provides a mathematical framework for understanding complex, self-similar shapes. The applications of fractal geometry range from computer graphics to financial modeling. Symmetrys practical applications extend to data visualization and cryptography. The article concludes by emphasizing symmetrys foundational role in physics, chemistry, computer graphics, and beyond. A deeper understanding of symmetry not only enriches perspectives across scientific disciplines but also fosters interdisciplinary collaborations, unveiling hidden order and structure in the natural and designed world. The exploration of symmetry promises ongoing discoveries at the intersection of mathematics and diverse fields of study.

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YUE, Y., J. H. XIE, and X. J. GAO. "CAPTURING THE SYMMETRY OF ATTRACTORS AND THE TRANSITION TO SYMMETRIC CHAOS IN A VIBRO-IMPACT SYSTEM." International Journal of Bifurcation and Chaos 22, no. 05 (May 2012): 1250109. http://dx.doi.org/10.1142/s021812741250109x.

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A three-degree-of-freedom vibro-impact system with symmetric two-sided constraints is considered. The system is strongly nonlinear and symmetric. The symmetric fixed point of the Poincaré map is deduced analytically, and the existence conditions of the symmetric fixed point are obtained. The six-dimensional Poincaré map can be expressed as the second iteration of another unsymmetric implicit map, which implies the symmetry of the Poincaré map. When the control parameter changes successively, symmetry-breaking bifurcation and symmetry-restoring bifurcation will occur at some point, and the attractor may change between symmetry and antisymmetry repeatedly. When a symmetry breaking bifurcation occurs, the symmetry is still the intrinsic property of the vibro-impact system. Here the Poincaré map cannot reflect the symmetry itself. However, the unsymmetric implicit map can capture a pair of antisymmetric ω-limit sets, which reflects the symmetry of the vibro-impact system. Different Poincaré sections are locally conjugate about a diffeomorphism. Therefore, as long as the perturbation is sufficiently small, changing the Poincaré section does not have any effect on the dynamical behavior. The transition to symmetric chaos is represented by numerical simulations.

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Shi, Zeyun, Jinkeng Lin, Jiong Chen, Yao Jin, and Jin Huang. "Symmetry Based Material Optimization." Symmetry 13, no. 2 (February 14, 2021): 315. http://dx.doi.org/10.3390/sym13020315.

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Many man-made or natural objects are composed of symmetric parts and possess symmetric physical behavior. Although its shape can exactly follow a symmetry in the designing or modeling stage, its discretized mesh in the analysis stage may be asymmetric because generating a mesh exactly following the symmetry is usually costly. As a consequence, the expected symmetric physical behavior may not be faithfully reproduced due to the asymmetry of the mesh. To solve this problem, we propose to optimize the material parameters of the mesh for static and kinematic symmetry behavior. Specifically, under the situation of static equilibrium, Young’s modulus is properly scaled so that a symmetric force field leads to symmetric displacement. For kinematics, the mass is optimized to reproduce symmetric acceleration under a symmetric force field. To efficiently measure the deviation from symmetry, we formulate a linear operator whose kernel contains all the symmetric vector fields, which helps to characterize the asymmetry error via a simple ℓ2 norm. To make the resulting material suitable for the general situation, the symmetric training force fields are derived from modal analysis in the above kernel space. Results show that our optimized material significantly reduces the asymmetric error on an asymmetric mesh in both static and dynamic simulations.

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MELKEMI, MAHMOUD, FREDERIC CORDIER, and NICKOLAS S. SAPIDIS. "A PROVABLE ALGORITHM TO DETECT WEAK SYMMETRY IN A POLYGON." International Journal of Image and Graphics 13, no. 01 (January 2013): 1350002. http://dx.doi.org/10.1142/s0219467813500022.

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This paper deals with the problem of detecting "weak symmetry" in a polygon, which is a special bijective and continuous mapping between the vertices of the given polygon. An application of this work is the automatic reconstruction of 3D polygons symmetric with respect to a plane from free-hand sketches of weakly-symmetric 2D polygons. We formalize the weak-symmetry notion and highlight its many properties which lead to an algorithm detecting it. The closest research work to the proposed approach is the detection of skewed symmetry. Skewed symmetry detection deals only with reconstruction of planar mirror-symmetric 3D polygons while our method is able to identify symmetry in projections of planar as well as nonplanar mirror-symmetric 3D polygons.

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Walsh, Toby. "Symmetry Breaking Constraints: Recent Results." Proceedings of the AAAI Conference on Artificial Intelligence 26, no. 1 (September 20, 2021): 2192–98. http://dx.doi.org/10.1609/aaai.v26i1.8437.

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Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful cases: symmetry breaking constraints for row and column symmetry, and symmetry breaking constraints for eliminating value symmetry.

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10

Narechania, Tejas. "Symmetry and (Network) Neutrality." Michigan Law Review Online, no. 119 (2020): 46. http://dx.doi.org/10.36644/mlr.online.119.46.symmetry.

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In this short Essay, I take the opportunity to highlight one further potential asymmetry that may yet emerge from the Supreme Court’s application of Chevron’s many doctrines. Drawing on then-Judge Kavanaugh’s disdissental from the D.C. Circuit’s decision affirming network neutrality rules, I suggest that there is at least one vote on the Supreme Court—and perhaps more—for an asymmetric approach to the major questions doctrine. Moreover, I demonstrate how asymmetry in this context is deeply irrational. As applied to network neutrality, the asymmetry has at least one of two effects. One, it might simply favor one large industry over another, subjecting one inter-sector wealth transfer to heightened scrutiny, while treating an analogous wealth transfer—in the opposite direction—deferentially. But the judiciary is not typically in the business of favoring one industrial sector over another. Two, it subjects consumer-protection devices to increased regulatory scrutiny, thereby shifting the costs and burdens of overcoming a regulatory default to those entities—consumers—who can likely least afford to bear them. Hence, in more general terms, Justice Kavanaugh’s unbalanced approach to the major questions doctrine tends to undermine many of the values— accountability and expertise, among others—that agency policymaking has long served.

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Iki, Kiyotaka, and Sadao Tomizawa. "Point-Symmetric Multivariate Density Function and Its Decomposition." Journal of Probability and Statistics 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/597630.

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For aT-variate density function, the present paper defines the point-symmetry, quasi-point-symmetry of orderk(<T), and the marginal point-symmetry of orderkand gives the theorem that the density function isT-variate point-symmetric if and only if it is quasi-point-symmetric and marginal point-symmetric of orderk. The theorem is illustrated for the multivariate normal density function.

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Chmyr’, S. N., A. S. Kazakov, A. V. Galeeva, D. E. Dolzhenko, A. I. Artamkin, A. V. Ikonnikov, N. N. Mikhailov, et al. "PT-Symmetric Microwave Photoconductivity in Heterostructures Based on the Hg1 − xCdxTe Topological Phase." JETP Letters 118, no. 5 (September 2023): 339–42. http://dx.doi.org/10.1134/s0021364023602385.

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The PT-symmetric photoconductivity has been detected for the first time in microwave-irradiated heterostructures based on thick Hg1 −xCdxTe films with the CdTe content x corresponding to the topological phase although the magnetic field symmetry (T symmetry) and the symmetry in the positions of potential contact pairs (P symmetry) are not conserved separately. The microwave photoconductivity in similar heterostructures based on the trivial Hg1 −xCdxTe phase is both P- and T-symmetric.

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13

Ma, Zhi Yong. "Research on Concept System of Rotation-Mirror Symmetry in Mechanical Systems." Applied Mechanics and Materials 201-202 (October 2012): 7–10. http://dx.doi.org/10.4028/www.scientific.net/amm.201-202.7.

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Mechanical rotation-mirror symmetry is grouped by rotation symmetry and mirror symmetry, and belongs to mechanical static structure symmetry. Collecting and Analyzing a lot of rotation-mirror symmetric instances, and referring to the researches on concept systems of rotation symmetry and mirror symmetry, the concept system of rotation-mirror symmetry was established. The concept system is classified by discrete mirror and continuous mirror rotation-mirror symmetry, unidirectional rotation and bidirectional rotation rotation-mirror symmetry, directed rotation and deflecting rotation rotation-mirror symmetry, entire rotation and partial rotation rotation-mirror symmetry. The concept system can completely contain all kinds of existence of rotation-mirror symmetry in mechanical systems.

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Kouyialis, Georgia, Xiaoyu Wang, and Ruth Misener. "Symmetry Detection for Quadratic Optimization Using Binary Layered Graphs." Processes 7, no. 11 (November 9, 2019): 838. http://dx.doi.org/10.3390/pr7110838.

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Symmetry in mathematical optimization may create multiple, equivalent solutions. In nonconvex optimization, symmetry can negatively affect algorithm performance, e.g., of branch-and-bound when symmetry induces many equivalent branches. This paper develops detection methods for symmetry groups in quadratically-constrained quadratic optimization problems. Representing the optimization problem with adjacency matrices, we use graph theory to transform the adjacency matrices into binary layered graphs. We enter the binary layered graphs into the software package nauty that generates important symmetric properties of the original problem. Symmetry pattern knowledge motivates a discretization pattern that we use to reduce computation time for an approximation of the point packing problem. This paper highlights the importance of detecting and classifying symmetry and shows that knowledge of this symmetry enables quick approximation of a highly symmetric optimization problem.

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Ma, Zhi Yong. "Research on Concept System of Mechanical Glide Symmetry." Applied Mechanics and Materials 151 (January 2012): 433–37. http://dx.doi.org/10.4028/www.scientific.net/amm.151.433.

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As one kind of mechanical static structure symmetry, glide symmetry is grouped by mirror symmetry and translation symmetry. Glide symmetry is widely exists in mechanical systems, and plays an important role in realizing the technical, economic and social performances of mechanical products. On the basis of research on the concept systems of mirror symmetry, translation symmetry and glide symmetric instances, and taking the characters of the different combined types of symmetry benchmarks as the standard, the concept system of mechanical glide symmetry was established, which can be the foundation of further researches on the application laws of glide symmetry in mechanical systems.

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Chuquichambi, Erick G., Guido B. Corradi, Enric Munar, and Jaume Rosselló-Mir. "When symmetric and curved visual contour meet intentional instructions: Hedonic value and preference." Quarterly Journal of Experimental Psychology 74, no. 9 (June 1, 2021): 1525–41. http://dx.doi.org/10.1177/17470218211021593.

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Symmetry and contour take part in shaping visual preference. However, less is known about their combined contribution to preference. We examined the hedonic tone and preference triggered by the interaction of symmetry and contour. Symmetric/curved, symmetric/sharp-angled, asymmetric/curved, and asymmetric/sharp-angled stimuli were presented in an implicit and explicit task. The implicit task consisted of an affective stimulus–response compatibility task where participants matched the stimuli with positive and negative valence response cues. The explicit task recorded liking ratings from the same stimuli. We used instructed mindset to induce participants to focus on symmetry or contour in different parts of the experimental session. We found an implicit compatibility of symmetry and curvature with positive hedonic tone. Explicit results showed preference for symmetry and curvature. In both tasks, symmetry and curvature showed a cumulative interaction, with a larger contribution of symmetry to the overall effect. While symmetric and asymmetric stimuli contributed to the implicit positive valence of symmetry, the effect of curvature was mainly caused by inclination towards curved contours rather than rejection of sharp-angled contours. We did not find any correlation between implicit and explicit measures, suggesting that they may involve different cognitive processing.

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He, Chen, Lei Wang, Yonghui Zhang, and Chunmeng Wang. "Dominant Symmetry Plane Detection for Point-Based 3D Models." Advances in Multimedia 2020 (October 27, 2020): 1–8. http://dx.doi.org/10.1155/2020/8861367.

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In this paper, a symmetry detection algorithm for three-dimensional point cloud model based on weighted principal component analysis (PCA) is proposed. The proposed algorithm works as follows: first, using the point element’s area as the initial weight, a weighted PCA is performed and a plane is selected as the initial symmetry plane; and then an iterative method is used to adjust the approximate symmetry plane step by step to make it tend to perfect symmetry plane (dominant symmetry plane). In each iteration, we first update the weight of each point based on a distance metric and then use the new weights to perform a weighted PCA to determine a new symmetry plane. If the current plane of symmetry is close enough to the plane of symmetry in the previous iteration or if the number of iterations exceeds a given threshold, the iteration terminates. After the iteration is terminated, the plane of symmetry in the last iteration is taken as the dominant symmetry plane of the model. As shown in experimental results, the proposed algorithm can find the dominant symmetry plane for symmetric models and it also works well for nonperfectly symmetric models.

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Locher, Paul J., and Johan Wagemans. "Effects of Element Type and Spatial Grouping on Symmetry Detection." Perception 22, no. 5 (May 1993): 565–87. http://dx.doi.org/10.1068/p220565.

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The influence of local and global attributes of symmetric patterns on the perceptual salience of symmetry was investigated. After tachistoscopic viewing, subjects discriminated between symmetric and either random patterns (experiment 1) or their perturbed counterparts (experiment 2) created by replacing one third of the mirror element-pairs of symmetric stimuli with ‘random’ elements. In general, it was found that perceptibility of symmetry, measured by response time and detection accuracy, was not influenced in a consistent way by type of pattern element (dots or line segments oriented vertically, horizontally, obliquely, or in all three orientations about the symmetry axis). Nor did axis orientation (vertical, horizontal, oblique), advance knowledge of axis orientation, practice effects, or subject sophistication differentially affect detection. A highly salient global percept of symmetry emerged, on the other hand, when elements were clustered together within a pattern, or grouped in symmetric pairs along a single symmetry axis or two orthogonal axes. Results suggest that mirror symmetry is detected preattentively, presumably by some kind of integral code which emerges from the interaction between display elements and the way they are organized spatially. It is proposed that symmetry is coded and signalled by the same spatial grouping processes as those responsible for construction of the full primal sketch.

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Ma, Zhi Yong. "Research on Existences and Concept System of Rotation Symmetry in Mechanical Systems." Applied Mechanics and Materials 148-149 (December 2011): 608–11. http://dx.doi.org/10.4028/www.scientific.net/amm.148-149.608.

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Rotation symmetry is a basic type of mechanical static structure symmetry, and plays an important role in mechanical systems. Based on collecting and analyzing rotation symmetric instances, the concept system of rotation symmetry classified by the directivity of symmetry components, the rotary type of symmetry components, the alternations of symmetry components, the distributing integrality of symmetry components and the type of symmetry benchmark was established, and was explained and verified by accurate instances. The concept system of rotation symmetry can offer the academic basis to the further research on the existent type, the application methods and the application laws of rotation symmetry in mechanical systems.

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Yue, Yuan, and Jian Huab Xie. "Symmetry Breaking and Symmetry Increasing in a Vibro-Impact with Symmetric Two-Sided Constraints." Applied Mechanics and Materials 66-68 (July 2011): 229–34. http://dx.doi.org/10.4028/www.scientific.net/amm.66-68.229.

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A three-degree-of-freedom vibro-impact system with symmetric two-sided constraints is considered. Existence conditions of the symmetric period -2 motion are given, and the symmetric period n-2 motion of the system is deduced analytically. The six dimensional Poincaré map is established, and the Jacobi matrix of the symmetrixc fixed point is obtained. By the numerical simulations, we show that symmetry breaking and symmetry increasing exists in the vibro-impact system with symmetric two-sided constraints.

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Li, Chunbiao, Jiayu Sun, Tianai Lu, and Tengfei Lei. "Symmetry Evolution in Chaotic System." Symmetry 12, no. 4 (April 5, 2020): 574. http://dx.doi.org/10.3390/sym12040574.

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A comprehensive exploration of symmetry and conditional symmetry is made from the evolution of symmetry. Unlike other chaotic systems of conditional symmetry, in this work it is derived from the symmetric diffusionless Lorenz system. Transformation from symmetry and asymmetry to conditional symmetry is examined by constant planting and dimension growth, which proves that the offset boosting of some necessary variables is the key factor for reestablishing polarity balance in a dynamical system.

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Heule, Marijn, and Toby Walsh. "Symmetry in Solutions." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (July 3, 2010): 77–82. http://dx.doi.org/10.1609/aaai.v24i1.7549.

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We define the concept of an internal symmetry. This is a symmety within a solution of a constraint satisfaction problem. We compare this to solution symmetry, which is a mapping between different solutions of the same problem. We argue that we may be able to exploit both types of symmetry when finding solutions. We illustrate the potential of exploiting internal symmetries on two benchmark domains: Van der Waerden numbers and graceful graphs. By identifying internal symmetries we are able to extend the state of the art in both cases.

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VAN SCHAFTINGEN, JEAN. "SYMMETRIZATION AND MINIMAX PRINCIPLES." Communications in Contemporary Mathematics 07, no. 04 (August 2005): 463–81. http://dx.doi.org/10.1142/s0219199705001817.

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We develop a method to prove that some critical levels for functionals invariant by symmetry obtained by minimax methods without any symmetry constraint are attained by symmetric critical points. It is used to investigate the symmetry properties of solutions of elliptic partial differential equations with Dirichlet or Neumann boundary conditions. It is also an alternative to concentration-compactness for some symmetric elliptic problems.

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Kudlicki, Andrzej, Małgorzata Rowicka, Mirosław Gilski, and Zbyszek Otwinowski. "An efficient routine for computing symmetric real spherical harmonics for high orders of expansion." Journal of Applied Crystallography 38, no. 3 (May 13, 2005): 501–4. http://dx.doi.org/10.1107/s0021889805007685.

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A numerically efficient method of constructing symmetric real spherical harmonics is presented. Symmetric spherical harmonics are real spherical harmonics with built-in invariance with respect to rotations or inversions. Such symmetry-invariant spherical harmonics are linear combinations of non-symmetric ones. They are obtained as eigenvectors of an appropriate operator, depending on symmetry. This approach allows for fast and stable computation up to very high order symmetric harmonic bases, which can be used in e.g. averaging of non-crystallographic symmetry in protein crystallography or refinement of large viruses in electron microscopy.

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Chaubey, Yogendra P., Govind S. Mudholkar, and M. C. Jones. "Reciprocal symmetry, unimodality and Khintchine’s theorem." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2119 (February 15, 2010): 2079–96. http://dx.doi.org/10.1098/rspa.2009.0482.

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The symmetric distributions on the real line and their multi-variate extensions play a central role in statistical theory and many of its applications. Furthermore, data in practice often consist of non-negative measurements. Reciprocally symmetric distributions defined on the positive real line may be considered analogous to symmetric distributions on the real line. Hence, it is useful to investigate reciprocal symmetry in general, and Mudholkar and Wang’s notion of R-symmetry in particular. In this paper, we shall explore a number of interesting results and interplays involving reciprocal symmetry, unimodality and Khintchine’s theorem with particular emphasis on R-symmetry. They bear on the important practical analogies between the Gaussian and inverse Gaussian distributions.

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Ke, Hong-Wei, Jia-Hui Zhou, Shuai Chen, Tan Liu, and Xue-Qian Li. "The hidden symmetries in the PMNS matrix and the light sterile neutrino(s)." Modern Physics Letters A 30, no. 27 (August 13, 2015): 1550136. http://dx.doi.org/10.1142/s0217732315501369.

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The approximately symmetric form of the PMNS matrix suggests that there could exist a hidden symmetry which makes the PMNS matrix different from the CKM matrix for quarks. In literature, all the proposed fully symmetric textures exhibit an explicit [Formula: see text] symmetry in addition to other symmetries which may be different for various textures. Observing obvious deviations of the practical PMNS matrix elements from those in the symmetric textures, there must be a mechanism to distort the symmetry. It might be due to the existence of light sterile neutrinos. As an example, we study the case of the Tribimaximal (TB) texture and propose that its apparent symmetry disappears due to the existence of a sterile neutrino.

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Podgorelec, David, Luka Lukač, and Borut Žalik. "Reflection Symmetry Detection in Earth Observation Data." Sensors 23, no. 17 (August 25, 2023): 7426. http://dx.doi.org/10.3390/s23177426.

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The paper presents a new algorithm for reflection symmetry detection, which is specialized to detect maximal symmetric patterns in an Earth observation (EO) dataset. First, we stress the particularities that make symmetry detection in EO data different from detection in other geometric sets. The EO data acquisition cannot provide exact pairs of symmetric elements and, therefore, the approximate symmetry must be addressed, which is accomplished by voxelization. Besides this, the EO data symmetric patterns in the top view usually contain the most useful information for further processing and, thus, it suffices to detect symmetries with vertical symmetry planes. The algorithm first extracts the so-called interesting voxels and then finds symmetric pairs of line segments, separately for each horizontal voxel slice. The results with the same symmetry plane are then merged, first in individual slices and then through all the slices. The detected maximal symmetric patterns represent the so-called partial symmetries, which can be further processed to identify global and local symmetries. LiDAR datasets of six urban and natural attractions in Slovenia of different scales and in different voxel resolutions were analyzed in this paper, demonstrating high detection speed and quality of solutions.

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Rahmani, Mohsen, Alexander S. Shorokhov, Ben Hopkins, Andrey E. Miroshnichenko, Maxim R. Shcherbakov, Rocio Camacho-Morales, Andrey A. Fedyanin, Dragomir N. Neshev, and Yuri S. Kivshar. "Nonlinear Symmetry Breaking in Symmetric Oligomers." ACS Photonics 4, no. 3 (February 16, 2017): 454–61. http://dx.doi.org/10.1021/acsphotonics.6b00902.

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Park, Chang-Joon, Kyung-Seok Seo, and Heung-Moon Choi. "Symmetric polarity in generalized symmetry transformation." Pattern Recognition Letters 27, no. 7 (May 2006): 854–57. http://dx.doi.org/10.1016/j.patrec.2005.11.010.

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Lee, Chee-hoon, Ho Jin Kim, and Joon Bum Kim. "Aortic symmetry index for symmetric repair." Journal of Thoracic and Cardiovascular Surgery 156, no. 4 (October 2018): 1397–98. http://dx.doi.org/10.1016/j.jtcvs.2018.05.106.

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Khan, Jamshed, Tahir Hussain, Dania Santina, and Nabil Mlaiki. "Homothetic Symmetries of Static Cylindrically Symmetric Spacetimes—A Rif Tree Approach." Axioms 11, no. 10 (September 26, 2022): 506. http://dx.doi.org/10.3390/axioms11100506.

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In this paper, we find all static, cylindrically symmetric spacetime metrics admitting homothetic symmetries. For this purpose, first we analyze the homothetic symmetry equations by an algorithm developed in Maple which gives all possible static, cylindrically symmetric metrics that may possess proper homothetic symmetry. After that, we have solved the homothetic symmetry equations for all these metrics to get the final form of homothetic symmetry vector fields. Comparing the obtained results with those of direct integration technique, it is observed that the Rif tree approach not only recovers the metrics already found by direct integration technique, but it also produces some new metrics.

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Li, Chunbiao, Julien Clinton Sprott, Yongjian Liu, Zhenyu Gu, and Jingwei Zhang. "Offset Boosting for Breeding Conditional Symmetry." International Journal of Bifurcation and Chaos 28, no. 14 (December 30, 2018): 1850163. http://dx.doi.org/10.1142/s0218127418501638.

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Symmetry is usually prevented by the broken balance in polarity. If the offset boosting returns the balance of polarity when some of the variables have their polarity reversed, the corresponding system becomes conditionally symmetric and in turn produces coexisting attractors with that type of symmetry. In this paper, offset boosting in one dimension or in two dimensions in a 3D system is made for producing conditional symmetry, where the symmetric pair of coexisting attractors exist from one-dimensional or two-dimensional offset boosting, which is identified by the basin of attraction. The polarity revision from offset boosting provides a general method for constructing chaotic systems with conditional symmetry. Circuit implementation based on FPGA verifies the coexisting attractors with conditional symmetry.

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Matthews, P. C. "Automating Symmetry-Breaking Calculations." LMS Journal of Computation and Mathematics 7 (2004): 101–19. http://dx.doi.org/10.1112/s1461157000001066.

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AbstractThe process of classifying possible symmetry-breaking bifurcations requires a computation involving the subgroups and irreducible representations of the original symmetry group. It is shown how this calculation can be automated using a group theory package such as GAP. This enables a number of new results to be obtained for larger symmetry groups, where manual computation is impractical. Examples of symmetric and alternating groups are given, and the method is also applied to the spatial symmetry-breaking of periodic patterns observed in experiments.

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Nomura, Toshio, Michael Ramek, and Bruno Gruber. "Programs for symmetry adaption coefficients for semisimple symmetry chains: the completely symmetric representations." Computer Physics Communications 61, no. 3 (December 1990): 410–32. http://dx.doi.org/10.1016/0010-4655(90)90054-5.

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Zhang, Hongjia, Junwen Huang, Xin Xu, Qiang Fang, and Yifei Shi. "Symmetry-Aware 6D Object Pose Estimation via Multitask Learning." Complexity 2020 (October 21, 2020): 1–7. http://dx.doi.org/10.1155/2020/8820500.

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Although 6D object pose estimation has been intensively explored in the past decades, the performance is still not fully satisfactory, especially when it comes to symmetric objects. In this paper, we study the problem of 6D object pose estimation by leveraging the information of object symmetry. To this end, a network is proposed that predicts 6D object pose and object reflectional symmetry as well as the key points simultaneously via a multitask learning scheme. Consequently, the pose estimation is aware of and regulated by the symmetry axis and the key points of the to-be-estimated objects. Moreover, we devise an optimization function to refine the predicted 6D object pose by considering the predicted symmetry. Experiments on two datasets demonstrate that the proposed symmetry-aware approach outperforms the existing methods in terms of predicting 6D pose estimation of symmetric objects.

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Friedman, Yaakov, and Tzvi Scarr. "Symmetry and Special Relativity." Symmetry 11, no. 10 (October 3, 2019): 1235. http://dx.doi.org/10.3390/sym11101235.

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We explore the role of symmetry in the theory of Special Relativity. Using the symmetry of the principle of relativity and eliminating the Galilean transformations, we obtain a universally preserved speed and an invariant metric, without assuming the constancy of the speed of light. We also obtain the spacetime transformations between inertial frames depending on this speed. From experimental evidence, this universally preserved speed is c, the speed of light, and the transformations are the usual Lorentz transformations. The ball of relativistically admissible velocities is a bounded symmetric domain with respect to the group of affine automorphisms. The generators of velocity addition lead to a relativistic dynamics equation. To obtain explicit solutions for the important case of the motion of a charged particle in constant, uniform, and perpendicular electric and magnetic fields, one can take advantage of an additional symmetry—the symmetric velocities. The corresponding bounded domain is symmetric with respect to the conformal maps. This leads to explicit analytic solutions for the motion of the charged particle.

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Chen, Yangyang, Yi Zhao, and Xinyu Han. "Characterization of Symmetry of Complex Networks." Symmetry 11, no. 5 (May 20, 2019): 692. http://dx.doi.org/10.3390/sym11050692.

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Recently, symmetry in complex network structures has attracted some research interest. One of the fascinating problems is to give measures of the extent to which the network is symmetric. In this paper, based on the natural action of the automorphism group Aut ( Γ ) of Γ on the vertex set V of a given network Γ = Γ ( V , E ) , we propose three indexes for the characterization of the global symmetry of complex networks. Using these indexes, one can get a quantitative characterization of how symmetric a network is and can compare the symmetry property of different networks. Moreover, we compare these indexes to some existing ones in the literature and apply these indexes to real-world networks, concluding that real-world networks are far from vertex symmetric ones.

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Ando, Shuji. "Orthogonal decomposition of the sum-symmetry model using the two-parameters sum-symmetry model for ordinal square contingency tables." Biometrical Letters 58, no. 2 (December 1, 2021): 105–17. http://dx.doi.org/10.2478/bile-2021-0008.

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Summary Studies have been carried out on decomposing a model with symmetric structure using a model with asymmetric structure. In the existing decomposition theorem, the sum-symmetry model holds if and only if all of the two-parameters sum-symmetry, global symmetry and concordancediscordance models hold. However, this existing decomposition theorem does not satisfy the asymptotic equivalence for the test statistic, namely that the value of the likelihood ratio chi-squared statistic of the sum-symmetry model is asymptotically equivalent to the sum of those of the decomposed models. To address this issue, this study introduces a new decomposition theorem in which the sum-symmetry model holds if and only if all of the two-parameters sum-symmetry, global symmetry and weighted global-sum-symmetry models hold. The proposed decomposition theorem satisfies the asymptotic equivalence for the test statistic—the value of the likelihood ratio chi-squared statistic of the sum-symmetry model is asymptotically equivalent to the sum of those of the two-parameters sum-symmetry, global symmetry and weighted global-sum-symmetry models.

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Chaudhary, Priyanka, and Akhilesh Kumar Mishra. "Switching dynamics in -symmetric structures with saturable cubic nonlinear response." Journal of Optics 23, no. 12 (November 12, 2021): 124003. http://dx.doi.org/10.1088/2040-8986/ac3299.

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Abstract In recent years, the field of -symmetry has witnessed a surge of research interest due to its ability to exploit even the losses of the system. -symmetry and its implications have been explored widely in the realm of photonics. In this work, we present a numerical investigation on the role of -symmetry in switching characteristics of a fibre Bragg grating (FBG) with cubic saturable nonlinear response. We have explored such FBGs in both -symmetric and broken -symmetric regimes. In addition, we have also studied the effect of -symmetry in switching characteristics of soliton pulse in directional coupler with saturable cubic nonlinear response and noticed that only unbroken regime provides switching in directional coupler.

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Vasanthy, G., and Stanley A. J. Pocock. "Radial through rotated symmetry of striate pollen of the Acanthaceae." Canadian Journal of Botany 64, no. 12 (December 1, 1986): 3050–58. http://dx.doi.org/10.1139/b86-404.

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In Nilgirianthus neilgherrensis (Bedd.) Brem. (tribe Strobilantheae) pollen grains normally have three "polar axially" oriented colpora and pseudocolpi (6 × 3), while a few are two, four, or five aperturate. Exinal features occasionally manifest different degrees of torsion and rotation. An abnormal two-colporate grain exhibits a peculiar 90° rotated symmetry, colpora, pseudocolpi, and sexinal ridges of one hemisphere being perpendicular to the other half. Bravaisia integerrima Standley and B. tubiflora Hemsl. (tribe Trichanthereae) have two-colporate, striate and rotationally symmetric pollen, except for a rare radially symmetric grain of B. integerrima. Two-colporate, striate pollen of Sanchezia lampra Leonard & Smith (tribe Trichanthereae) has also rotated symmetry, but anomalous grains exhibit radial orientation and divergent rotations of exinal features. These divergencies in orientation could be the gradations between polar axial – radial symmetry and 90°-rotated symmetry. This surmise raises several points of discussion such as the role of plasmalemma or factors controlling variable symmetry within a taxon or an anther, effectiveness of rotational symmetry as an harmomegathus, and the significance of the trend, change of symmetry, observed in the striate palynomorphs of different plant lineages and geological periods.

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Selzer, M. I. "'Symmetry' for Bilateral Symmetry." Notes and Queries 58, no. 3 (August 10, 2011): 417–19. http://dx.doi.org/10.1093/notesj/gjr128.

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Tjan, Bosco S., and Zili Liu. "Symmetry impedes symmetry discrimination." Journal of Vision 5, no. 10 (December 13, 2005): 10. http://dx.doi.org/10.1167/5.10.10.

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JIANG, QINGTANG. "BIORTHOGONAL WAVELETS WITH SIX-FOLD AXIAL SYMMETRY FOR HEXAGONAL DATA AND TRIANGLE SURFACE MULTIRESOLUTION PROCESSING." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 05 (September 2011): 773–812. http://dx.doi.org/10.1142/s0219691311004316.

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This paper discusses the construction of highly symmetric compactly supported wavelets for hexagonal data/image and triangle surface multiresolution processing. Recently, hexagonal image processing has attracted attention. Compared with the conventional square lattice, the hexagonal lattice has several advantages, including that it has higher symmetry. It is desirable that the filter banks for hexagonal data also have high symmetry which is pertinent to the symmetric structure of the hexagonal lattice. The high symmetry of filter banks and wavelets not only leads to simpler algorithms and efficient computations, it also has the potential application for the texture segmentation of hexagonal data. While in the field of computer-aided geometric design (CAGD), when the filter banks are used for surface multiresolution processing, it is required that the corresponding decomposition and reconstruction algorithms for regular vertices have high symmetry, which make it possible to design the corresponding multiresolution algorithms for extraordinary vertices. In this paper we study the construction of six-fold axial symmetric biorthogonal filter banks and the associated wavelets, with both the dyadic and [Formula: see text]-refinements. The constructed filter banks have the desirable symmetry for hexagonal data processing. By associating the outputs (after one-level multiresolution decomposition) appropriately with the nodes of the regular triangular mesh with which the input data is associated (sampled), we represent multiresolution analysis and synthesis algorithms as templates. The six-fold axial symmetric filter banks constructed in this paper result in algorithm templates with desirable symmetry for triangle surface processing.

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Pramod, R. T., and S. P. Arun. "Symmetric Objects Become Special in Perception Because of Generic Computations in Neurons." Psychological Science 29, no. 1 (December 8, 2017): 95–109. http://dx.doi.org/10.1177/0956797617729808.

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Symmetry is a salient visual property: It is easy to detect and influences perceptual phenomena from segmentation to recognition. Yet researchers know little about its neural basis. Using recordings from single neurons in monkey IT cortex, we asked whether symmetry—being an emergent property—induces nonlinear interactions between object parts. Remarkably, we found no such deviation: Whole-object responses were always the sum of responses to the object’s parts, regardless of symmetry. The only defining characteristic of symmetric objects was that they were more distinctive compared with asymmetric objects. This was a consequence of neurons preferring the same part across locations within an object. Just as mixing diverse paints produces a homogeneous overall color, adding heterogeneous parts within an asymmetric object renders it indistinct. In contrast, adding identical parts within a symmetric object renders it distinct. This distinctiveness systematically predicted human symmetry judgments, and it explains many previous observations about symmetry perception. Thus, symmetry becomes special in perception despite being driven by generic computations at the level of single neurons.

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McBeath, Michael K., Diane J. Schiano, and Barbara Tversky. "Three-Dimensional Bilateral Symmetry Bias in Judgments of Figural Identity and Orientation." Psychological Science 8, no. 3 (May 1997): 217–23. http://dx.doi.org/10.1111/j.1467-9280.1997.tb00415.x.

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The two experiments reported explored a bias toward symmetry in judging identity and orientation of indeterminate two-dimensional shapes Subjects viewed symmetric and asymmetric filled, random polygons and described “what each figure looks like” and its orientation Viewers almost universally interpreted the shapes as silhouettes of bilaterally symmetric three-dimensional (3-D) objects This assumption of 3-D symmetry tended to constrain perceived vantage of the identified objects such that symmetric shapes were interpreted as straight-on views, and asymmetric shapes as profile or oblique views Because most salient objects in the world are bilaterally symmetric, these findings are consistent with the view that assuming 3-D symmetry can be a robust heuristic for constraining orientation when identifying objects from indeterminate patterns

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Sievers, Silvan, Martin Wehrle, Malte Helmert, and Michael Katz. "Strengthening Canonical Pattern Databases with Structural Symmetries." Proceedings of the International Symposium on Combinatorial Search 8, no. 1 (September 1, 2021): 91–99. http://dx.doi.org/10.1609/socs.v8i1.18429.

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Symmetry-based state space pruning techniques have proved to greatly improve heuristic search based classical planners. Similarly, abstraction heuristics in general and pattern databases in particular are key ingredients of such planners. However, only little work has dealt with how the abstraction heuristics behave under symmetries. In this work, we investigate the symmetry properties of the popular canonical pattern databases heuristic. Exploiting structural symmetries, we strengthen the canonical pattern databases by adding symmetric pattern databases, making the resulting heuristic invariant under structural symmetry, thus making it especially attractive for symmetry-based pruning search methods. Further, we prove that this heuristic is at least as informative as using symmetric lookups over the original heuristic. An experimental evaluation confirms these theoretical results.

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Ellison, Tyler D., Kohtaro Kato, Zi-Wen Liu, and Timothy H. Hsieh. "Symmetry-protected sign problem and magic in quantum phases of matter." Quantum 5 (December 28, 2021): 612. http://dx.doi.org/10.22331/q-2021-12-28-612.

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We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic to study the complexity of symmetry-protected topological (SPT) phases of matter. In particular, we say a state has a symmetry-protected sign problem or symmetry-protected magic, if finite-depth quantum circuits composed of symmetric gates are unable to transform the state into a non-negative real wave function or stabilizer state, respectively. We prove that states belonging to certain SPT phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, we find that one-dimensional Z2×Z2 SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional Z2 SPT states (e.g. Levin-Gu state) have symmetry-protected magic. Furthermore, we comment on the relation between a symmetry-protected sign problem and the computational wire property of one-dimensional SPT states. In an appendix, we also introduce explicit decorated domain wall models of SPT phases, which may be of independent interest.

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Kaplan, Ilya G. "Modern State of the Pauli Exclusion Principle and the Problems of Its Theoretical Foundation." Symmetry 13, no. 1 (December 24, 2020): 21. http://dx.doi.org/10.3390/sym13010021.

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The Pauli exclusion principle (PEP) can be considered from two aspects. First, it asserts that particles that have half-integer spin (fermions) are described by antisymmetric wave functions, and particles that have integer spin (bosons) are described by symmetric wave functions. It is called spin-statistics connection (SSC). The physical reasons why SSC exists are still unknown. On the other hand, PEP is not reduced to SSC and can be consider from another aspect, according to it, the permutation symmetry of the total wave function can be only of two types: symmetric or antisymmetric. They both belong to one-dimensional representations of the permutation group, while other types of permutation symmetry are forbidden. However, the solution of the Schrödinger equation may have any permutation symmetry. We analyze this second aspect of PEP and demonstrate that proofs of PEP in some wide-spread textbooks on quantum mechanics, basing on the indistinguishability principle, are incorrect. The indistinguishability principle is insensitive to the permutation symmetry of wave function. So, it cannot be used as a criterion for the PEP verification. However, as follows from our analysis of possible scenarios, the permission of states with permutation symmetry more general than symmetric and antisymmetric leads to contradictions with the concepts of particle identity and their independence. Thus, the existence in our Nature particles only in symmetric and antisymmetric permutation states is not accidental, since all symmetry options for the total wave function, except the antisymmetric and symmetric, cannot be realized. From this an important conclusion follows, we may not expect that in future some unknown elementary particles that are not fermions or bosons can be discovered.

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Tsvetkov, S. V. "Non-Linear Constitutive Equations for Transversely Isotropic Materials Belonging to the С∞ and С∞h Symmetry Groups." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 84 (June 2019): 46–59. http://dx.doi.org/10.18698/1812-3368-2019-3-46-59.

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Transversely isotropic materials feature infinite-order symmetry axes. Depending on which other symmetry elements are found in the material structure, five symmetry groups may be distinguished among transversely isotropic materials. We consider constitutive equations for these materials. These equations connect two symmetric second-order tensors. Two types of constitutive equations describe the properties of these five material groups. We derived constitutive equations for materials belonging to the C∞ and C∞h symmetry groups in the tensor function form. To do this, we used corollaries of Curie's Symmetry Principle. This makes it possible to obtain a fully irreducible form of the tensor function.

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Shabbir, Ghulam, F. M. Mahomed, and M. A. Qureshi. "Proper projective symmetry in the most general non-static spherically symmetric four-dimensional Lorentzian manifolds." International Journal of Geometric Methods in Modern Physics 13, no. 02 (January 26, 2016): 1650009. http://dx.doi.org/10.1142/s0219887816500092.

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A study of proper projective symmetry in the most general form of non-static spherically symmetric space-time is given using direct integration and algebraic techniques. In this study, we show that when the above space-time admits proper projective symmetry it becomes a very special class of static spherically symmetric space-times.

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Journal articles on the topic 'Symmetry'

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